{"paper":{"title":"A dendrite generated from {0,1}^{\\Lambda}, Card\\Lambda \\succ \\aleph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Akihiko Kitada, Shousuke Ohmori, Tomoyuki Yamamoto","submitted_at":"2014-02-15T13:40:30Z","abstract_excerpt":"The existence of a decomposition space with a dendritic structure of a topological space $(\\{0,1\\}^\\Lambda ,\\tau_{0}^\\Lambda )$ is discussed. Here, $\\Lambda $ is any set with the cardinal number $\\succ \\aleph , \\{0,1\\}^{\\Lambda }=\\{\\varphi :\\Lambda \\rightarrow \\{0,1\\}\\}, \\tau_0$ is the discrete topology for $\\{0,1\\}$ and the topology $\\tau_0^{\\Lambda }$ for $\\{0,1\\}^\\Lambda $ is the topology with the base $\\beta =\\{<G_{\\lambda _1},\\dots,G_{\\lambda _n}>~;~G_{\\lambda_1}\\in \\tau_0,\\dots,G_{\\lambda _n}\\in \\tau_0, \\{\\lambda _1,\\dots,\\lambda _n\\}\\subset \\Lambda ,n\\in {\\bf N}\\}$ where the notation $<"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7309","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}